Servo compensation including a non-linear synchro transmitter

ABSTRACT

A conventional synchro device; including a rotor, a stator, a three-phase winding and a single phase winding, is modified by the addition of a trim winding which is inductively coupled to the three phase winding and provides non-linear operation of the synchro. The trim winding is electrically coupled to the single phase winding to provide a null indication when the respective output voltages from these windings are substantially equal. In order to obtain the null indication, output angle data from the synchro must vary in a non-linear manner with respect to applied input angle data. An additional shorted damping winding, may be inductively coupled to the single phase winding and the trim winding to produce a flux which counteracts flux induced in the single phase and trim windings thereby reducing the voltages in the trim winding and the single phase winding. The voltage in the single phase winding is reduced to a greater extent than the voltage in the trim winding and the non-linearity between the input angle data and the output angle data over limited ranges of input angle is further increased.

United States Patent [1 1 Boynton et al.

[ SERVO COMPENSATION INCLUDING A NON-LINEAR SYNCHRO TRANSMITTER [75]Inventors: Richard P. Boynton; Robert C. Ellis,

Jr., both of Durham, N.C.

[73] Assignee: Sperry Rand Corporation, New

York, N.Y.

22 Filed: Dec. 10,1970

[21] Appl.No.: 96,873

[56] References Cited UNITED STATES PATENTS 2,603,696 7/1952 McEwan..3l8/692 X 2,814,767 11/1957 Gray ..3l8/633 3,234,444 2/1966 Burmeisteret al. .....318/633 OTHER PUBLICATIONS Resolver Handbook, Reeves Inst.Corp., Rico Bulletin No. 57, Copyright 1954, Assorted pages.

ATT l TUDE REFERENCE SOURCE ATTITUDE I SIGNAL g MONlTOR 1 March 6, 1973Primary Examiner-T. E. Lynch Attorney-S. C. Yeaton [57] ABSTRACT Aconventional synchro device; including a rotor, a stator, a three-phasewinding and a single phase winding, is modified by the addition of atrim winding which is inductively coupled to the three phase winding andprovides non-linear operation of the synchro. The trim winding iselectrically coupled to the single phase winding to provide a nullindication when the respective output voltages from these windings aresubstantially equal. In order to obtain the null indication, outputangle data from the synchro must vary in a non-linear manner withrespect to applied input angle data. An additional shorted dampingwinding, may be inductively coupled to the single phase winding and thetrim winding to produce a flux which counteracts flux induced in thesingle phase and trim windings thereby reducing the voltages in the trimwinding and the single phase winding. The voltage in the single phasewinding is reduced to a greater extent than the voltage in the trimwinding and the nonlinearity between the input angle data and the outputangle data over limited ranges of input angle is further increased.

7 Claims, 4 Drawing Figures ATTITUDE INDICATOR 32 NULL SENSOR COMPARATORMONITOR SOURCE DEMOD W l l PATENIEBIIIR 6 m5 SHEET 2 OF 3 ATTITUDEINDICATOR 20 EXCITATION MOTOR NULL SENSOR |COMPARATOR MONITOR 41 I I l lI I I l l MONITOR DEMOD ATTITUDE REFERENCE SOURCE ATTITUDE SIGNAL SOURCEROBERT C. ELL/5 JR.

ATTORNEY PATENTEBHAR 61973 3 9,

SHEET 30F 3 I INVE/VTU/PS R/CHARD P. aoy/vra/v ROBERT c. ELL/.5 JR.

A TTORNEY SERVO COMPENSATION INCLUDING A NON- LINEAR SYNCIIROTRANSMITTER BACKGROUND OF THE INVENTION 1. Field of the Invention Thepresent invention pertains to the field of variable transformers whichare a class of magnetic field transducers. More specifically, theinvention is applicable to those devices commonly known as synchros andin- .cludes control transformers, control transmitters and differentialtransmitters among others.

2. Description of the Prior Art The prior art devices include a stator,a rotor, an input winding and an output winding. These windings arewound on a magnetic structure usually in combina-v tions of single phaseand three phase windings. For example, a control transmitter may have asingle phase winding on the rotor and a three-phase winding on thestator. The term phase in reference to synchros generally refers to theangular position of the various windings and does not refer to timephase. When an input alternating voltage is applied to the single phaserotor winding, it induces voltages in the three-phase stator windinghaving magnitudes and polarities which uniquely define a resulting anglethat is a function of the input angular position of the rotor withrespect to the stator.

In a control transformer, the three-phase winding and the single phasewinding are mounted in the same manner as in the control transmitter.The alternating input voltages are applied to the three-phase statorwinding and uniquely define an input angle which induces an alternatingvoltage in the rotor winding. The rotor winding voltage is proportionalto the difference between the input angle and the resulting mechanicalangular position of the rotor with respect to the stator. In thesedevices, the resulting angle is linearly related to the input angle. 7

Where it has been desired to have a particular range of output anglevary slightly in response to large variations in angular input or have aa particular range of output angle vary greatly in response to smallvariations in angular input, conventional synchro devices have beenfound to be insufficient.

Applications for devices having a non-linear relationship betweenapplied input angle data and produced output angle data include aircraftindicator instruments. For example, during flight only course control ofan aircraft may be desired. Thus, an indicator may be required toprovide a small output displacement in response to a first input signalof a given magnitude whereas during a landing maneuver flying control ofthe aircraft is desired and the same indicator may be required toprovide a large output displacement in response to a second input signalhaving the same magnitude as the first input signal. A prior art devicewhich enables an indicator to provide such non-linear operation isdisclosed in U.S. Pat. No. 3,316,532 entitled Aircraft Follow-UpServo-Mechanism Indicating Apparatus" issued Apr. 25, 1967 to Richard E.Schaffer and assignedto the same assignee as the subject invention.Prior art devices such as that disclosed in U.S. Pat. No. 3,316,532required complex apparatus which included feedback circuitry or aplurality of synchros, to obtain a non-linear angular relationshipbetween the input angle data and the output angle data. The nonlinearsynchro disclosed herein is an improvement over the apparatus describedin U.S. Pat. No. 3,316,532.

SUMMARY OF THE INVENTION The present invention is a synchro devicehaving at least one trim winding in addition to the conventionalthree-phase and single phase windings thereby providing a non-linearrelationship between applied input angle data and produced output angledata. The trim winding is inductively coupled to the three-phase windingand electrically coupled to the single phase winding so that the fluxproduced by the three phase winding induces voltages in both the singlephase winding and the trim winding. A null voltage occurs when theinstantaneous trim winding voltage is equal to the instantaneous singlephase winding voltage. For given values of applied input angle datasuccessive null voltages are obtained for values of output angle datawhich are nonlinear functions of the applied input angle data. Thedegree of non-linearity is controlled by varying the ratio of themaximum voltage induced in the trim winding to the maximum voltageinduced in the single phase winding to obtain a null voltage. Furthercontrol of this non-linearity may be obtained by providing at least oneshorted damping winding that is inductively coupled to the single phasewinding to produce a flux which reduces the total flux within thesynchro. As a result, the magnitudes of the trim winding and the singlephase winding maximum voltages are also reduced. By appropriate designof the shorted damping winding, its effect on the single phase windingvoltage may be varied with respect to its effect on the trim windingvoltage thereby providing expansion and contraction of the non-linearrelationship between the input angle data and the output angle data overspecific ranges of input angle data.

This invention enables reduction in the cost and the complexity of servomechanism apparatus which provide angle output data as a non-linearfunction of the angle input data.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. ii is a schematic drawing of aconventional synchro transformer including the invention.

FIG. 2 is a graph of input angle data versus output angle data of theinvention without the shorted damping winding for three different ratiosof E E FIG. 3 is a schematic drawing of an attitude indicatorincorporating the invention.

FIG. 4 is a graph of the transfer characteristic of the inventionincorporated in the attitude indicator.

DESCRIPTION OF THE PREFERRED EMBODIMENT As shown in FIG. 1, a non-linearsynchro 10 includes a conventional synchro transformer comprised ofthree stator mounted wye connected windings 11, 12 and 13, and a rotorwinding 14. A first winding added to the conventional synchrotransformer windings is a trim winding 15 which is wound in quadraturewith a stator winding. FIG. ll shows the trim winding 15 wound inquadrature with the stator winding 12. A second winding, which is addedto the rotor, is a damping winding 16 shown with its output terminals Dand D shorted together. The trim winding 15 is electrically coupled tothe rotor winding 14 through a null meter 17 which provides a nullindication when there is a minimum difference between the outputvoltages on terminals '1, and T, of the trim winding 15 and terminals R,and R of the rotor winding 14.

In a conventional synchro transformer an alternating three-phaseelectrical signal which defines an input angle is applied to inputterminals S, S, and S of the stator windings l1, l2 and 13. A resultingvoltage is provided at the output terminals R and R of the rotor winding14 which is proportional to the sine of the difference angle A0 betweenthe angle 0 of the applied electrical signal and the mechanical angle 6of the synchro electrical signal and the mechanical angle 0 of thesynchro transformer rotor with respect to the synchro transformerstator. Subsequently, the shaft on which the rotor is wound rotatesuntil the mechanical angle 0 is equal to the angle 0 of the appliedelectrical signal. The voltage provided at the output terminals R and Rbecomes zero because the difference angle A0 is zero. Therefore, in theconventional synchro transformer, the output angle 0, is essentiallyequal to the input angle 0,,, i.e., the output angle 0,, is a linearfunction of the input angle 0 In order to simplify the explanation ofthe invention, the effect of the trim winding 15 and the null meter 17will be disussed initially, and the description of the damping winding16 will be presented subsequently. The output angle 0,, will beredefined as the mechanical angle 0,, required to obtain a nullindication on the null meter 17 for any angle 0 of an applied threephaseelectrical signal. The expression for the output voltage across theterminals R, and R is:

in which:

E maximum rotor winding output voltage A0 1ml 0! The expression for theoutput voltage across terminals T, and T is E1 E Sin 0 in which: Emaximum trim winding output voltage 0,, angle defined by the appliedthree-phase electrical signal.

Since a null indication will be obtained on the null meter 17 when thedifference between the rotor winding output voltage E and the trimwinding output voltage E is zero, then E equals E Substituting the aboveexpressions:

E0 Sin E Sin 0 Sin (E E Sin 0 the degree of non-linearity as representedby sin A0 is proportional to the product of the ratio of the maximumtrim winding output voltage to the maximum rotor winding output voltageand the sine of the input angle 0,,,

FIG. 2 shows a plot of the input angle 0 against the the output angle 0for three different ratios of [E E It will be observed that the degreeof nonlinearity increases as this ratio increases. Generally, the

slope of the plot increases from linearity i.e., (E E 0, for values ofinput angle between 0-90 and for values between 270360, whereas forvalues between 270bL it decreases.

The damping winding 16 is wound in phase with the rotor winding 14 andits function is to reduce the amount of flux within the synchro 10. Themagnitude of this reduction is controlled by two factors: The firstbeing the volume of copper employed in constructing the damping winding16 and the second, the percentage of flux within the synchro 10 thatlinks the damping winding 16. The former is a function of the length andthe diameter of the copper in the damping winding 16 and the latter is afunction of the spatial positioning of the turns in the winding 16 withrespect to the stator winding and the rotor winding. The trim voltage Eand the rotor winding voltage E, are reduced by the addition of thedamping winding 16. However, each will vary in a different manner. Thesevariations may be expressed as functions of the difference angle A0 as:

ET: (ETM Sin 0-) [f1( o 01u A0 if:

since the rotor winding 14 and the trim winding 15 are connected toprovide zero output when the rotor winding voltage equals the trimwinding voltage, then:

( m Sin 1") [f1 on Sin [f2 for zero voltage output. In thisconfiguration the damping winding 16 is wound in phase and on the rotorwith the rotor winding 14 it is therefore closer in proximity to therotor winding 14 than to the trim winding 15, as a result it willprovide a greater reduction in the induced voltage in the rotor winding14 than in the induced voltage in the trim winding 15. This reduction isnonlinear over limited ranges of input angle 0 From the foregoing it canreadily be appreciated by those skilled in the art that there is a widelatitude for selecting combinations involving the parameters E E f (A0)and f (A0) to obtain non-linear variations in expansion and contractionof the plot of the input angle 0 against the output angle 0 An alternateembodiment of the subject invention will be described with reference toFIG. 1. In the alternate embodiment, the damping winding 16 iseliminated and damping is obtained by using an unbalanced three-phasewinding in the non-linear synchro 10. For example, the windings 11 and13 would comprise N number of turns and the winding 12 would be KNnumber of turns in which K is a factor greater or less than unity. Whenthe non-linear synchro 10 with an unbalanced three-phase winding 12 isused as a CT, the variation in load impedance which the non-linearsynchro 10 presents to a transmitter is reduced. Further, if thenon-linear synchro 10 is coupled to a signal voltage source having anappreciable source impedance, lower null voltages are obtainable byusing the non-linear synchro 10 having an unbalanced threephase winding12.

In operation, a non-linear synchro 10 having an unbalanced three-phasewinding 12 is unbalanced such that at a zero input angle, no flux isproduced by the unbalanced winding 12. Thus, the gradient or degree ofnon-linearity is essentially the same as would be obtained with nodamping. As the input angle is varied from zero, the component of fluxproduced by the unbalanced winding 12 provides a successively largerpercentage of the total flux in the non-linear synchro 10. Therefore,the total flux varies as a function of the input angle, increasing thevoltage induced in the output winding 14. The trim winding 15 isdisposed so that the component of flux linking it is less sensitive tothis change in flux thereby changing the ratio of the voltage across theterminals R and R with respect to the voltage across the terminals T andT thus providing damping of the output voltage across the terminals Rand R This ratio iscontrollable over a wide range of variation asdetermined by the factor K and the other physical parameters of thenon-linear synchro 10, such as the number of turns N and the relativeplacement of the windings.

A specific application of this device is an attitude sensor as shown inFIG. 3. This sensor is fabricated to produce a two to one expansion ofthe output angle 0 over 0 to 30 of input angle 0, with the furtherrequirement that for a value of input angle equal to 85, the outputangle must be less than 129. The plot of the input angle 0,, against theoutput angle 0,, for the nonlinear synchros 22 and 23 incorporated inFIG. 3 is shown in FIG. 4. As can be seen from this plot, these devicesmeet the imposed requirements.

In the attitude sensor 20, an attitude signal source 21 provides athree-phase signal which defines an input angle 0, The non-linearsynchro 22 includes threephase rotor windings 23, 24 and 25 which areconnected to the three-phase input signal 0 A trim winding 26 is alsomounted on the rotor with the threephase windings 23, 24 and 25, inquadrature with the winding 25 and coupled to a demodulator 27. A firstsingle phase stator winding is electrically coupled to the trim winding26 and the demodulator 27. The demodulator 27 senses any difference inoutput voltage from the trim winding 26 and the first stator winding 304 and applies an error signal voltage to an amplifier 31. The amplifier31 increases the magnitude of the error signal which is used to controlmotor 32. The shaft of the motor 32 is mechanically coupled to the rotorof the synchro 22, the rotor of a second synchro 33 and a pitchindicator device 32. The second synchro 33 includes rotor and statorwindings as described above in synchro 22. An attitude reference source46 provides a three-phase reference signal which defines a referenceangle 0,. Three-phase windings 34, 35 and 36 are mounted on the rotor ofthe synchro 33 and respond to the three-phase attitude reference signal.A trim winding 37 is also mounted on the rotor of synchro 33 inquadrature with the winding 36 as shown in FIG. 3. A first single phasewinding 40 on the stator of the synchro 33 is electrically coupled tothe trim winding 37 and a null sensor indicator in a comparator monitor41.

A second single phase winding 42 identical to stator winding 30 is alsowound on the stator of the synchro 6 22 for providing an output voltagewhen the difference between the angle input signal 0,, and themechanical angle of the synchro rotor is less than 90 with respect tothe stator. in this embodiment the windings 25 and 36 are unbalanced andfunction in place of a shorted single phase winding to act as a dampingwinding to provide control of the non-linear relationship between thevoltages induced in the trim winding 26, the first single phase winding30, the trim winding 37 and the first single phase winding 40.

The function of the second synchro 33 is to indicate when a null ispresent between the angles defined by the attitude reference signalreceived from the attitude reference source 46 and the mechanicalangular displacement produced by the motor 32. When these angles areequal in magnitude, the output voltage in the trim winding 37 will beequal to the output voltage in the first single phase winding 40 and anull indication will be produced by the null sensor in the comparatormonitor 41. A second single phase winding 44 mounted on the stator ofthe synchro 33 produces an output when the difference between the angle0, and the mechanical angle of the synchro rotor is less than Thisoutput provides a visual indication that excitation is present in theexcitation monitor of the comparator monitor 41. The signals sensed bythe comparator monitor 41 will indicate if an excitation and a null arepresent thereby verifying the correctness of the pitch indication indisplay 32. If, however, the reference angle is not the same as themechanical angle, the null sensor will not indicate a null and, if theexcitation to synchro 33 is lost, the excitation monitor will detect afailure by loss of the excitation indication and cause a warning signalto be produced.

While the invention has been described in its preferred embodiment, itis to be understood that the words which have been used are words ofdescription rather than limitation and that changes may be made withinthe purview of the appended claims without departing from the true scopeand spirit of the invention in its broader aspects.

We claim:

1. in an attitude indicator device coupled to an attitude signal sourceand an attitude reference source, a

0 first servo mechanism comprising a synchro device including a rotor,

single phase Wye-connected winding means mounted on said rotor andcoupled to said attitude signal source,

trim winding means mounted on said rotor and wound in quadrature withone of said Wye-connected winding means,

a stator,

first single phase winding means mounted on said stator and electricallycoupled to said trim winding means for producing an error voltage outputin the absence of a null voltage across said series combination,

a second single phase winding means wound on said stator in quadraturewith said first single phase winding means having a voltage inducedwhenever the difference between said input angle data and said outputangle data is less than 90,

monitor means coupled to said single phase winding for providing avisual indication when excitation is present in said single phasewinding,

motor means responsive to said error voltage output and mechanicallycoupled to said rotor for providing non-linear angular displacement ofsaid rotor to reduce said error voltage to a null, and

display means coupled to said motor means for providing a visualindication of said non-linear angular displacement which produces saidnull.

2. In an attitude indicator device as described in claim 1 saidcombination including a second servo mechanism coupled to said attitudereference course comprising a synchro device having a rotor,

single phase Wye-connected winding means mounted on said rotor andcoupled to said attitude reference source, said rotor being mechanicallycoupled to said motor means and said synchro device in said first servomechanism,

trim winding means mounted on said rotor and wound in quadrature withone of said single phase Wye-connected winding means,

first single phase winding means mounted on said stator, and

null sensing means coupled between said trim winding means and saidfirst single phase winding means for indicating a null when saidattitude reference source provides a signal that defines an angle equalin magnitude to said non-linear angular displacement of said rotor insaid first servo mechanism.

3. A synchro device for providing output angle data which is anon-linear function of applied input angle data comprising a stator,

single phase Wye-connected winding means mounted on said stator andresponsive to said applied input angle data for producing a primary fluxwithin said device,

a rotor disposed within said stator for producing output angle data inaccordance with the angular position of said rotor with respect to saidstator,

single phase winding means mounted on said rotor for producing rotorvoltages in response to said flux, and

single phase winding means mounted on said stator in quadrature with oneof said single phase wyeconnected winding means and connected in serieswith said single phase rotor winding means, said single phase trimwinding means includes means for producing voltages of magnitudes equalto said induced rotor voltages at angular positions of said rotor, saidpositions varying at a greater angular rate than said applied inputangle data over an initial range of input angle, at a lesser angularrate over an intermediate range of input angle and at a greater angularrate over a terminal range of input angle.

4. A synchro device as described in claim 3 in which said single phasetrim winding means further includes means for producing a ratio betweenthe maximum value of trim voltage induced in said single phase trimwinding means and the maximum value of voltage induced in said singlephase rotor winding means which controls the angular rate at which saidrotor angular positions are varied.

5. A synchro device as described in claim 3 which further includesshorted damping winding means mounted on said rotor for producing fluxwhich reduces said induced rotor voltages at a greater rate than saidinduced trim voltages thereby roviding additional control of the angularrate at whrc said ro or angular positions are varied.

6. A synchro device as described in claim 3 in which said Wye-connectedsingle phase winding means include two windings having an equal numberof turns and a third winding having a greater number of turns forproducing an increasing percentage of total flux in said synchro as saidinput angle data changes from zero thereby providing additional controlof the angular rate at which said rotor angular positions are varied.

7. A synchro device as described in claim 6 in which said Wye-connectedsingle phase winding means includes two windings having an equal numberof turns and a third winding having a lesser number of turns.

1. In an attitude indicator device coupled to an attitude signal sourceand an attitude reference source, a first servo mechanism comprising asynchro device including a rotor, single phase wye-connected windingmeans mounted on said rotor and coupled to said attitude signal source,trim winding means mounted on said rotor and wound in quadrature withone of said wye-connected winding means, a stator, first single phasewinding means mounted on said stator and electrically coupled to saidtrim winding means for producing an error voltage output in the absenceof a null voltage across said series combination, a second single phasewinding means wound on said stator in quadrature with said first singlephase winding means having a voltage induced whenever the differencebetween said input angle data and said output angle data is less than90*, monitor means coupled to said single phase winding for providing avisual indication when excitation is present in said single phasewinding, motor means responsive to said error voltage output andmechanically coupled to said rotor for providing non-linear angulardisplacement of said rotor to reduce said error voltage to a null, anddisplay means coupled to said motor means for providing a visualindication of said non-linear angular displacement which produces saidnull.
 1. In an attitude indicator device coupled to an attitude signalsource and an attitude reference source, a first servo mechanismcomprising a synchro device including a rotor, single phasewye-connected winding means mounted on said rotor and coupled to saidattitude signal source, trim winding means mounted on said rotor andwound in quadrature with one of said wye-connected winding means, astator, first single phase winding means mounted on said stator andelectrically coupled to said trim winding means for producing an errorvoltage output in the absence of a null voltage across said seriescombination, a second single phase winding means wound on said stator inquadrature with said first single phase winding means having a voltageinduced whenever the difference between said input angle data and saidoutput angle data is less than 90*, monitor means coupled to said singlephase winding for providing a visual indication when excitation ispresent in said single phase winding, motor means responsive to saiderror voltage output and mechanically coupled to said rotor forproviding non-linear angular displacement of said rotor to reduce saiderror voltage to a null, and display means coupled to said motor meansfor providing a visual indication of said non-linear angulardisplacement which produces said null.
 2. In an attitude indicatordevice as described in claim 1 said combination including a second servomechanism coupled to said attitude reference course comprising a synchrodevice having a rotor, single phase wye-connected winding means mountedon said rotor and coupled to said attitude reference source, said rotorbeing mechanically coupled to said motor means and said synchro devicein said first servo mechanism, trim winding means mounted on said rotorand wound in quadrature with one of said single phase wye-connectedwinding means, first single phase winding means mounted on said stator,and null sensing means coupled between said trim winding means and saidfirst single phase winding means for indicating a null when saidattitude reference source provides a signal that defines an angle equalin magnitude to said non-linear angular displacement of said rotor insaid first servo mechanism.
 3. A synchro device for providing outputangle data which is a non-linear function of applied input angle datacomprising a stator, single phase wye-connected winding means mounted onsaid stator and responsive to said applied input angle data forproducing a primary flux within said device, a rotor disposed withinsaid stator for producing output angle data in accordance with theangular position of said rotor with respect to said stator, single phasewinding means mounted on said rotor for producing rotor voltages inresponse to said flux, and single phase winding means mounted on saidstator in quadrature with one of said single phase wye-connected windingmeans and connected in series with said single phase rotor windingmeans, said single phase trim winding means includes means for producingvoltages of magnitudes equal to said induced rotor voltages at angularpositions of said rotor, said positions varying at a greatEr angularrate than said applied input angle data over an initial range of inputangle, at a lesser angular rate over an intermediate range of inputangle and at a greater angular rate over a terminal range of inputangle.
 4. A synchro device as described in claim 3 in which said singlephase trim winding means further includes means for producing a ratiobetween the maximum value of trim voltage induced in said single phasetrim winding means and the maximum value of voltage induced in saidsingle phase rotor winding means which controls the angular rate atwhich said rotor angular positions are varied.
 5. A synchro device asdescribed in claim 3 which further includes shorted damping windingmeans mounted on said rotor for producing flux which reduces saidinduced rotor voltages at a greater rate than said induced trim voltagesthereby providing additional control of the angular rate at which saidrotor angular positions are varied.
 6. A synchro device as described inclaim 3 in which said wye-connected single phase winding means includetwo windings having an equal number of turns and a third winding havinga greater number of turns for producing an increasing percentage oftotal flux in said synchro as said input angle data changes from zerothereby providing additional control of the angular rate at which saidrotor angular positions are varied.